New Combinatorial Complete One-Way Functions

Abstract

In 2003, Leonid A. Levin presented the idea of a combinatorial
complete one-way function and a sketch of the proof that Tiling
represents such a function. In this paper, we present two new
one-way functions based on semi-Thue string rewriting systems and a
version of the Post Correspondence Problem and prove their
completeness. Besides, we present an alternative proof of Levin's
result. We also discuss the properties a combinatorial problem
should have in order to hold a complete one-way function.